Surely you’ve seen these around:

You don’t really understand something unless you can explain it to your grandmother in three sentences or less.

or, apparently by Rutherford:

An alleged scientific discovery has no merit unless it can be explained to a barmaid.

I’ll call this idea the paragraph postulate: that you understand something only if you can explain it, in a single paragraph, to someone that doesn’t know the first thing about it (judging from the quotes, preferably a woman).

While fairly common in popular culture, the paragraph postulate is wrong, and bordering on dangerous.

1.

In the book linked above, the paragraph postulate is presented only to be refuted immediately: it’s been outdated by Einstein’s new discoveries. Nobody seriously expects general relativity (or, to be fair to the quote, just any of the core ideas of general relativity) to be explainable in a paragraph to someone with no prior knowledge at all on the subject.

And it’s not because it’s physics, and physics is specially hard. Sure, physics is hard. But other fields are also hard, and the paragraph postulate isn’t just wrong when used about physics (or other math-heavy disciplines). If you don’t know anything about philosophy, getting to Kant’s transcendental idealism is going to take more than three sentences.

Even if you succeed in summarizing a complex idea in a paragraph, the result is likely to be a technically correct definition that is completely useless to anyone who doesn’t know what you’re talking about.

A monad is a way to structure computations in terms of values and sequences of computations using those values. Monads allow the programmer to build up computations using sequential building blocks, which can themselves be sequences of computations. The monad determines how combined computations form a new computation and frees the programmer from having to code the combination manually each time it is required.

(From the Haskell wiki. All clear now?)

A point of note with the paragraph postulate is that its level of wrongness is tied to the gap between the learner’s knowledge and what is being explained. You can’t explain general relativity to any random person in a paragraph, but maybe you can if you’re explaining it to a specialist of differential analysis. Conversely, you may be successful explaining Newton’s three laws to a general layman, but you would have a ton of trouble explaining them to someone who doesn’t have a concept of physical laws or the scientific method.

So maybe a salvageable version of the paragraph postulate is that you shouldn’t try to explain something to someone if a minimum viable explanation takes more than a paragraph.

2.

Why does this matter? Because the idea that anything worth saying should be so simple as to not require more than a paragraph of explanations, besides being wrong, has poor consequences.

The paragraph postulate encourages distrust in experts. Maybe we can’t (or don’t yet now how to) make a reasonable argument as to why we think climate change is a real, human-caused phenomenon in a paragraph; that doesn’t mean we should ignore it. (Of course, this shouldn’t be taken as a free pass on jargon either)

More generally, the paragraph postulates justifies intellectual laziness: “if this idea isn’t explained in a limpid way in a paragraph, I should make no effort to understand it since clearly the author himself doesn’t get it”.

3.

Of course, this is not to say that you should not try to explain things in the simplest possible terms. I also absolutely do think that being able to explain something more simply is a sign of better understanding.

As an example, many mathematical proofs of new results are very long and complex at first, only accessible to mathematicians in the top of their subfield; as understanding of the subject (and related notions) grows, these progressively get simplified, often to the point of ending up understandable by undergrads. Here’s an interesting list of examples.

But we should not treat human knowledge as so shallow it can be summed up as a list of disconnected three-sentence ideas.